The HCF of two numbers is `16` and their product is `3072` . Find their LCM.

Options

A. `185`
B. `192`
C. `172`
D. None of these

Answer

To find the LCM of two numbers given their HCF and product, we can use the relationship between HCF, LCM, and the product of the two numbers. The formula we will use is:

\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]

### Step-by-Step Solution:

1. **Identify the given values:**
- HCF = 16
- Product of the two numbers = 3072

2. **Use the formula:**
- According to the formula:
\[ \text{HCF} \times \text{LCM} = \text{Product} \]
We can substitute the known values into the formula:
\[ 16 \times \text{LCM} = 3072 \]

3. **Rearrange the formula to solve for LCM:**
- To find LCM, we can rearrange the equation:
\[ \text{LCM} = \frac{\text{Product}}{\text{HCF}} \]

4. **Substitute the values into the rearranged formula:**
\[ \text{LCM} = \frac{3072}{16} \]

5. **Perform the division:**
- Now, we calculate:
\[ 3072 \div 16 = 192 \]

6. **Conclusion:**
- Therefore, the LCM of the two numbers is:
\[ \text{LCM} = 192 \]

### Final Answer:
The LCM of the two numbers is **192**.

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